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Synthesis and characterization of coreshell structure
silicacoated Fe29.5Ni70.5 nanoparticles
M Ammar1, F Mazaleyrat1,4, J P Bonnet2, P Audebert2, A Brosseau2, G Wang3
and Y Champion3
1SATIE, ENS Cachan, CNRS, UniverSud, 61 av President Wilson, F94230 CACHAN, France.
2PPSM, ENS Cachan, CNRS, UniverSud, 61 av President Wilson, F94230 CACHAN, France.
3CECM CNRSUPR 2801, 15 rue Georges Urbain 94407 VitrysurSeine, France
4IUFM de Créteil, rue Jean Macé, F94861 BonneuilsurMarne, France
EMail : [email protected] cachan.fr
Abstract
In view of potential applications of magnetic particles in biomedicine and electromagnetic
devices, we made use of the classical Stöber method – basecatalysed hydrolysis and
condensation of tetraethoxysilane (TEOS) – to encapsulate FeNi nanoparticles within a silica
shell. An original stirring system under high power ultrasounds made possible to disperse the
otherwise agglomerated particles. Sonication guaranteed particles to remain dispersed during
the Stöber synthesis and also improved the efficiency of the method. The coated particles are
characterized by electron microscopy (TEM) and spectroscopy (EDX) showing a coreshell
structure with a uniform layer of silica. Silicacoating does not affect the core magnetic
properties. Indeed, all samples are ferromagnetic at 77 K and room temperature and the Curie
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point remains unchanged. Only the coercive force shows an unexpected nonmonotonous
dependence on silica layer thickness.
1. Introduction
Magneticmetal nanoparticles encapsulated in a dielectric inorganic material are considered to
have practical applications in electromagnetic devices, biology and fundamental study to
improve the local physical investigation of magnetic nanostructures. In the coreshell
structure, the core sizedependant magnetic susceptibility at room temperature combined with
the chemical stability of the silica coatings suggests that the resulting nanocomposite may be
a good candidate for biomedical applications, such as magnetic separation, drug targeting,
image contrast in magnetic resonance imaging and hyperthermia therapy [1,2,3]. Magnetic
fluids dedicated for clinical applications are typically colloidal suspensions of iron, magnetite,
ironnickel and cobalt nanoparticles coated with biocompatible surfactants [4]. Actually, there
are two fundamental criteria to prevent the catalysis of damaging reactions within cells, the
reduction of the toxicity of the vector conveying the solution due to its oxidative alteration
and its chemical time stability. Accordingly, the silica coating of magnetic nanoparticles is
one of promising tool to ensure this specific biocompatibility and leads to low toxicity
material.
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Magneticdielectric nanocomposites have also attracted sustained interest over one century
owing to their unusual combined magnetic and electric properties. In fact, due to their
metallic nature, eddy currents limit application of magnetic nanoparticles at high frequency.
The coating by an insulating shell on the surface of soft magnetic nanoparticle cores such as
FeNi confers to the material a high permeability independent of the frequency even in GHz
range [5]. Such materials are typically suited for applications in telecommunication [6]. On
the other hand, the ability to control magnetic interactions is an important consequence of the
coating of magnetic particles, which has been explored in details by several authors for
particles in solution [7] and closepacked thin films [8]. Coating thickness controls both
insulation of nanoparticles and interparticle distance and, therefore, the interparticle
interactions [9]. This provided substantially reliable results to study magnetic nanostructure of
nanoparticles using electron holography [10].
Several synthetic routes for producing magnetic nanoparticles have been explored during the
last decade including chemical vapor condensation (CPVD), powder pyrolysis and
sonochemical synthesis [11,12,13]. However, nanoparticles synthesized by these methods
frequently display a relatively poor cristallinity or polydispersity in their shape or/and size,
which affects their magnetic properties. Evaporation–cryocondensation process has been
developped to overcome some of these problems. In the present work, cryogenic melting has
been used to produce Fe29.5Ni70.5 nanoparticles and consequently to guarantee more
cristallinity and a better stability in the elemental chemical composition. Additionally,
several approaches, such as the solgel process [14], coprecipitation [15,16,17], metal
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dielectric cosputtering deposition [18] or metal ion deposition, have been used to prepare
magneticinsulator nanocomposites. Our present approach is to start from metallic
nanoparticles and to coat them with an inorganicdielectric polymer in order to control the
morphology of the shell. In this paper, a modified Stöber approach has been used to
encapsulate in silica the asprepared metallic FeNi particles. In fact, we have introduced high
power sonochemistry not only in the dispersion step, but also during the synthesis to improve
the effectiveness of the classical Stöber method [19,20].
2. Experimental details
Synthesis of Fe29.5Ni70.5 nanoparticles
FeNi nanoparticles with welldefined morphology and homogeneous chemical composition
were synthesised using the cryogenic melting technique. This method consists in sliding down
a feeding bar of metal (Fe29.5Ni70.5) into a Radio Frequency (RF) reactor. A drop of molten
metal forms at the edge and falls onto the inductors where it is levitated to complete
transformation into nanocrystalline powders. In order to have sufficient vapour pressure, the
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metal must be heated up by several hundred degrees over its melting temperature (over
2000°C for Fe, Ni). The size of particle depends critically on the metal vapour pressure. The
gas produced from the cryogenic liquid carry the particles into a canvas filter. Technical
details are reported in [21]. The asobtained ironnickel nanopowders are composed of
spherical particles with an average diameter of about 55 nm (deduced from microscopy,
standard deviation 20 nm). From Electron Energy Loss Spectroscopy (EELS) the chemical
composition is homogeneous from one particle to another as well as inside the nanoparticles.
The fraction of iron x = 0.295 is of particular interest since large amounts can be produced
with no deviation in chemical composition [22]. Because metallic nanoparticles are
pyrophoric in air, they are collected in hexane where an oxide layer of approximately 2 nm
forms, making possible their manipulation without risk. The magnetization of asprepared
ironnickel particles (75 Am2/kg) is 20% lower compared to the bulk alloy magnetization,
which confirms the nonmagnetic nature of the oxide layer observed from electron
microscopy and analysed using XPS (XRay Photoemission Spectroscopy). Essentially Nickel
Hydroxides Ni(OOH) and Ni(OH2), iron oxide Fe2O3 and FeO were detected [22].
Synthesis of Silicacoated Fe29.5Ni70.5 nanoparticles
The silica shell onto FeNi core was synthesized according to the Stöber method [23] (solgel
reaction) without any silane coupling agent (like 3aminopropyltrimethoxysilane which is
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sometimes used for noble metals nanoparticules silica coating [24]). Indeed, oxide shell
covering FeNi nanoparticles is expected to enhance the SiO2 shell binding.
Ethanol (9596% synthesis grade) and Ammonia solution (28% analytical grade) were
purchased from SDS/CARLO ERBA, tetraethylorthosilicate (TEOS) ≥ 98% (GC) from
FLUKA. All reagents were used as received without further purification.
Ultrasonic dispersion was carried out with a Bandelin 200W (variable from 10 to 100%)
ultrasonic processor (Sonopuls HD 2200) fitted out with a horn of 13×3 mm. All experiments
were made in glass flask equipped with a cooling jacket to keep the mixture temperature
constant.
Typically, 80 mg of raw Fe29.5Ni70.5 nanoparticles were first sonicated in 50 ml of ethanol
during 90 minutes under a controlled ultrasonic power of 3 W/cm3. Then, various volumes of
TEOS and ammonia 28% (NH4OH) were successively introduced into the suspension and the
mixture was again sonicated for 90 minutes under a power of 0.5 W/cm3 to complete the sol
gel reaction (Figure 1). Finally the suspensions are centrifuged at 3000 rpm for 10 minutes,
the solvent is discarded, and the FeNi nanoparticles are ultrasonically redispersed in 50 ml of
ethanol. This purification process (centrifugation/dispersion under sonication) was repeated
three times. The particles were then transferred into ethanol to avoid any further growth or
chemical modification of the silica layer. Subsequently, an amount of the coated nanoparticles
were dried under reduced pressure and moderate temperature to remove remaining solvent
and to prepare samples for the physical characterization. Four samples with different reagent
concentrations have been produced (see table 1).
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Characterization and techniques
Thermal degradation analyses were made with a PerkinElmer Pyris 6TGA instrument using
standard ceramic crucibles and sample mass of 129mg. The samples were heated at a rate of
10 °C min1 from room temperature to 1000 °C in an air flow of 10 ml min1 or an argon flow
of 80 ml min1. The analyser was coupled to a permanent magnet producing a gradient field in
the crucible to measure the Curie temperature (Tc). These measurements are conducted under
argon flow to avoid adventitious oxidation of the nanoparticles. Fourier Transform InfraRed
spectra (FTIR) were recorded with a Thermoelectron Corporation NEXUS spectrometer
equipped with an attenuated total reflectance probe (ATR) covering the wavenumber range
4000700 cm1. The morphology and size of the particles were analysed by conventional and
high resolution electron microscopy (HRTEM) using a TECNAI F20 microscope (operating
at 200 kV with a pointtopoint resolution of 0.24 nm), on the powders deposited onto a
microscopy grid coated with an amorphous carbon film. Powders were also characterized by
Electron Energy Loss Spectra (EELS) in a Gatan Image Filter (GIF 2000) spectrometer
coupled to the TECNAI F20. Fitting and integration windows of 30 eV were used for all the
chemical maps and the spectra were obtained with an energy resolution of 1.2 eV. Elemental
chemical analysis of the nanocomposites was also performed using Energy Dispersive Xrays
(EDX) attached to the same system. The quasistatic hysteresis loops with an applied
magnetic field of –300 kA/m < H < 300 kA/m were acquired using a homemade Vibrating
Sample Magnetometer (VSM) between room and liquid nitrogen temperature.
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3. Results and discussion
Fourier Transform Infrared (FTIR) spectroscopy was used to identify the functional groups
present on the surface of FeNi@SiO2 nanoparticles. Comparison of uncoated and silica
coated particles FTIR spectra (Figure 2) shows a pronounced change detected in the 1300
700 cm1 region, which clearly indicates the presence of the silica coating. The peaks at 970
and 1070 cm1 correspond to the characteristic SiOSi bond, typically attributed to the SiO
symmetric stretching and SiOSi asymmetric stretching respectively, in agreement with [25].
Analysis of bonding configurations from FTIR data suggest also the existence of SiOC
or/and ≡SiOSi≡ functions (bands under 1000 cm1). Nevertheless, the spectra are obviously
dominated by the SiOSi bonding vibrations, for all coated samples. The presence of this
type of strained bond is a clear evidence of the mechanical stress in the silica sheath, which in
turn may strain the FeNi nanoparticles.
The chemical composition was examined using Energy–Dispersive Xray (EDX)
spectroscopy, which shows a Fe29.5Ni70.5 core coated by silica shell (Figure 3). The copper
lines in this figure are due to the copper grid used as TEM sample holder. An atomic ratio of
Si/O = 1/0.6 was obtained on the coreshell structure, indicating that the offstoichiometric
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silica shell is siliconrich in nature. The structural evolution study suggests that the silica layer
grows without affecting the integrity of the FeNi core. Indeed, the spectra do not reveal other
elements except those present initially in the FeNi core, the oxide layer, the silica shell and
the copper grid.
Figure 4 shows TEM pictures of FeNi@SiO2 particles synthesized using various TEOS
volumes. Observation of figure 4 images (a), (b), (c) and (d) clearly shows the shell thickness
dependence on TEOS concentration (see also table 1). Additionally Energy Filtered in
scanning TEM mode, which one can see an illustration on the inset (f) of figure 4, comes to
support the elementary chemical nature of the silicalayer surrounding the nanoparticles. In
fact, the image exhibits a chemical cartography obtained from EELS and undeniably shows
the formation of silica uniformly on the FeNi core.
The properties of oxidationresistance of the FeNi@SiO2 composite were tested by TGA.
Figure 5 shows the typical curves of thermal analysis of metallic materials [26].
Correspondingly, the weight increment of the coated particles (sample 5) caused by FeNi
oxidation decreased from 28% to 5% relative to that of the uncoated FeNi particles (sample
1). It is clear that a thicker shell of silica can protect the nickeliron from oxidation more
efficiently. For instance the oxidation of the FeNi core of FeNi@SiO2 composites (sample 4)
proceeds at ~430 °C which is 250 °C higher than for asprepared FeNi nanoparticles. The
weight loss, observed for coated samples starting from RT, is attributed to the surface
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dehydration of the silica monolayer and the loss of others organic compounds which are
volatile in this range of temperature [27].
For many applications of coreshell particles, such as electromagnetic devices [28], it is of
essential importance to control precisely the thickness of the shell. In the system under
consideration, the simplest approach to vary shell thickness is to use different amounts of
TEOS. Consequently, we investigate the effect of adding various amounts of TEOS in a
single step. Figure 4 (e), which features a typical high resolution image (HRTEM) for sample
4, reveals a coreshell structure with an uniform amorphous silica coating (thickness 15 nm).
For comparison, the thickness of silicashell is deduced from magnetic characterization. In
fact, the volume of SiO2 can be estimated using
−==
)(
)(122
2
2Frees
Coateds
MMmm
VSiO
Coated
SiO
SiO
SiO ρρ
where V and m are for volume and weight, respectively, ρSiO2 is the silica density estimated
experimentally (2270 kg/m3) and Ms(Am2/kg) is the specific magnetic moment at saturation;
“coated” indicates the coated sample, and “free” corresponds to the raw FeNi powder.
Assuming that the nanoparticles are monodisperse and 55 nm in diameter, the theoretical
thickness tMAG required to increase the radius R of the seed particle to a final radius R+tMAG is
given by [29]
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−
+= 113 2
FeNi
FeNiSiO
MAG mV
Rtρ
where 2SiOCoatedFeNimmm −= is the weight of the effective magnetic component in the
nanocomposite. The bulk Fe29.5Ni70.5 density was used (8450 kgm3 [30]).
Figure 6 shows the dependence of the thickness of silica shell, deduced from TEM analysis
and magnetic measurements, on TEOS volume. Interestingly, the two data are consistent with
a quantitative silica formation on the nanoparticles for thin silica layer up to 20 nm. Above
this limit tMAG presents a discrepancy compared to tTEM for thicker silica layer (beyond 20 nm).
This could be explained by the presence of free silica nanoparticles synthesized when a large
amount of TEOS is added. After centrifugation, the calculated volumic amount of silica
coating the nanoparticles is underrated and therefore, the deduced silicashell thickness is
erroneous.
4. Magnetic properties
The TGA recordings under constant magnetic field are presented in figure 7. Due to the
neutral atmosphere (argon flow), oxidation was inhibited. Up to 600 °C we observe a weak
weight drop due to a chemical desorption from the silica shell for coated particles as reported
in [27]. Comparable weight loss is observed for uncoated sample 1 due to the desorption of
organic chains adsorbed in the oxidized FeNi surface during the passivation step of the
nanoparticles. The TGA traces show a characteristic feature for all samples which reveals a
typical ferromagnetictoparamagnetic transition at the Curie temperature (Tc). Noticeably,
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the nanocomposites (sample 2 to 5) exhibit a broaden transition. Obviously, this makes
difficult the extraction of Tc which roughly maintains a stable value of 605 °C (± 5 °C) for all
samples in agreement with the literature [31].
A comparative measurement of hysterisis loops at 300 K (RT) and 77 K was performed for
both uncoated and silicacoated nanoparticles using VSM as mentioned previously.
Magnetization curves are reported in figure 8 and the main quantities are listed in table 2
(specific saturation magnetization, remanent magnetization and coercivity at 77 K and RT).
All curves at RT saturate approximately at the same applied field than those measured at
77 K. For the same operating temperature, loops for coated samples appear to have a
component whose magnetization continues to increase with increasing field up to 200 kA/m,
whereas the raw FeNi powder saturates much faster than the nanocomposites. In fact the
interparticle interactions are modulated by the thickness of the coating layer which isolates
the particles. As a result the nanocomposite hardens magnetically and its saturation becomes
difficult [6,18,32]. For all samples there is only a slight deviation regarding the saturation
magnetization between 77 K and RT because RT/Tc 0.3. Furthermore, ≈ the coating quality is
examined in saturation magnetization versus silicalayer thickness plots as an inset in figure 8
(right side). It is clearly seen that the specific magnetization decreases with increasing the
thickness of silicashell. Accordingly diamagnetic contribution of silica leads to a lower
saturation magnetization than the corefree FeNi particles (table 2).
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The inset, left side of figure 8, illustrates the coercive field versus the thickness of silicashell
at 77 K and RT. Noticeably, the temperature dependence of coercivity indicates a slight
increase for all samples when temperature decreases which is consistent with an increase of
anisotropy regardless of its origin. On the one hand, for randomly oriented nanoparticles with
cubic anisotropy, the coercive field should be Hc ≈ 0.64K1/Js [33]. If we consider the bulk
Fe30Ni70 magnetocristalline anisotropy K1 700 J/m≈ 3 [34] and the measured saturation
magnetization Js = 0.8 T, we find Hc 560 A/m≈ which is in disagreement with the
experimental coercivity. On the other hand, the morphology and size effect are believed to be
the reason of high coercivity observed for all samples (22 kA/m < Hc < 32 kA/m, see table 2).
According to the pioneering work of Néel [35], for soft magnetic nanoparticles
a dissymmetry of some atomic layers is sufficient in order to make the contribution of
demagnetizing field becoming dominant and to lead to an enhancement of the coercivity.
Shape anisotropy effect is due to the asphericity of the nanoparticles below a critical size.
The coercive field in an elongated spheroidal singledomain particle is given by Hc=2Ks/Js
[36] where ( )
0
2
2µsab
sJNNK −= is the shape anisotropy. Nb and Na represent the demagnetizing
coefficients along the two axes of an ellipsoid of revolution [37]. For an asphericity
0.86<γ<1.14,
−= γ
54
59
31
aN and since 12 =+ ba NN we find 0
2
5)1(
µγ s
sJK −= (γ>1).
Consequently, we deduce
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( )0512
µγ s
cJH −=
If we assume a coercive field Hc = 33 kA/m, we find an asphericity of 13%. The result is
consistent with TEM observations (figure 4) where 0.80<γ<1.2 was found. The coercive field
dependence on silica layer thickness shows a nonmonotonous evolution. For thin silicalayer
a sensitive drop in coercivity is observed followed by an increase before recovering the initial
value. This is probably due to a competition between dipoledipole interaction and magneto
elastic anisotropy. In the one hand, dipolar interactions are reduced as the distance between
magnetic cores is increasing. In the other hand, it has been shown by FTIR the existence of
stress in the silica shell. As the thickness of the shell increases, the stress experienced at the
surface of FeNi nanoparticles is enhanced yielding an increasing magnetoelastic anisotropy.
These two contributions balanced for a thickness of ~15 nm. Classically, for ultrafine
nanoparticles (~10 nm or less) dispersed in nonmagnetic material, anhysteretic loops are
expected because of the superparamagnetic behavior of the nanoparticles, as already reported
[38,39]. For the FeNi nanoparticles described in this paper, the shape anisotropy dominates
the magnetocristalline anisotropy (Ks = 20 kJ/m3 >> K1) so the critical size for which the
superparamagnetism is observed at room temperature is given by
nmK
TkD
s
Bsp 27
1503 ≈=
π
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compared with nmK
TkB 721503
1
≈π [40], where T is the measuring temperature and kB the
Boltzmann constant. Considering the mean size of the nanoparticles (55 nm), this is in line
with the hysteresis observed for all samples (figure 8). Because part of the particles is smaller
than 27 nm and because some are nearly spheroidal (γ<1.05) a superparamagnetic
contribution is not excluded. Another interesting feature is the remarkable stability of the
squareness ratio regardless of temperature and coating (see table 2). The Mr/Ms ratio is
noticeably lower than 0.5 predicted for single domain particles according to Néel and Stoner
[41,42]. Actually, this low value is typical of vortexlike magnetic structure composed of an
out of the plane uniformly magnetized core surrounded by a crown of curling spins [10].
Alternatively to a coherent rotation, the magnetization process consists initially into an
irreversible switch of the vortex core followed by a screwlike rotation of the external curling
spins [43].
5. Conclusions and perspectives
The preparation of silicacoated FeNi particles was successfully achieved by a combination of
two original synthetic procedures, a cryogenic evaporation of master alloy Fe29.5Ni70.5 to obtain
nanoparticles with welldefined size and composition, and subsequently a modified classical
Stöber method which permits to encapsulate the latter within a silica shell. The coating can be
accomplished through a direct, simple, onestep procedure. FTIR, EDX and EELS analysis
are consistent with the presence of silica in the nanocomposites synthesized. Consequently the
silicashell thickness could be conveniently controlled through the TEOS volume added to the
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colloidal FeNi solution. Our study allowed us to correlate the shellsilica thickness with the
evolution of the magnetic properties of the final nanocomposite. The magnetic investigations
demonstrate the possibility of making propertytunable magnetic nanoparticles ready for
surface engineering in particular with bioactive molecules or for electromagnetic device
applications aiming to enhance frequency limits. These aspects will undoubtedly require
further longerterm ageing studies. In particular, the chemical stability must be ensured before
any invivo applications are intended. Electronic holography experiments are in course to
confirm the expected vortex structure of the FeNi nanoparticles.
Acknowledgements
This work was supported by the Institut d’Alembert IFRCNRSUMR 8531, 61 Av. Du
President Wilson 94235 Cachan, France.
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Figure Captions
Figure 1. Illustration of the silicacoated Fe29.5Ni70.5 nanoparticles stepwise synthesis protocol.
Figure 2. Thermal gravimetric curves (TGA) of FeNi@SiO2 nanocomposites (sample 1 to 5)
under air flow. Thermal nanopowder alteration obviously depends on the amount of silica in
the sample.
Figure 3. FTIR spectra recorded from different samples FeNi@SiO2 (sample 1 to 5) related to
various volumes of TEOS in range of 7502500 cm1. The main resonances are identified in
the figure and discussed in the text in relation with the dominating SiOSi vibrations on solid
surface.
Figure 4. In the inset of top, EDX spectrum of Fe29.5Ni70.5 corefree nanoparticles. In the inset
of bottom, EDX of silica portion of a FeNi@SiO2 nanoparticles when the beam was focused
on silica edges.
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Figure 5. (ad) Representative transmission electron micrographs of the silicacoated FeNi
nanoparticles corresponding respectively to the sample 1, 2, 4, 5 (e) HRTEM pattern for the
silica@FeNi (sample 3) which shows the presence of a 15 nm thick silica layer lying at the
particle surface (f) Typical EFTEM analysis using metallic silicon as the silica source (Si K
edge), displays the chemical cartography showing a silicarich shell (sample 3).
Figure 6. Plot of silicalayer thickness as function of various volume of precursor TEOS,
estimated from HRTEM analysis (tTEM) and magnetic characterization (tMAG) (see also table 1).
Figure 7. Thermal gravimetric curves (TGA) of FeNi@SiO2 nanocomposites (sample 1 to 5)
under argon flow. See table 2 for Curie temperatures assessed from curves.
Figure 8. Magnetic quasistatic hysterisis loops for samples with various silicashells (sample
1 to 5). On the left, magnetization curves recorded at 300 K. The inset on the lower right
corner illustrates the changes in the Ms as a function of the silicashell thickness. On the right
the M–H curves recorded at 77 K. The inset on the lower right corner illustrates the changes
in the coercive field as a function of the silicashell thickness.
20
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Table 1. Summary of the FeNi@SiO2 synthesis, presenting the various volumes of reagents
used. The Silicalayer thickness was estimated using HRTEM analysis (tTEM) and magnetic
investigation (tMAG).
Silica Coating (after dispersion
under ultrasounds (3 w/cm3)) t (nm)
TEOS(µl) NH4OH(ml) tTEM tMAG
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
0
50
100
200
500
0
0.35
0.7
1.4
3.5
0
3
8
15
33
0
4
9
17
24
21
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Table 2. Magnetic properties for uncoated FeNi (sample 1) and silicacoated FeNi (sample 2
to 5) nanoparticles. Ms is the specific saturation magnetization, Mr remanent magnetization, Tc
Curie temperature and Hc coercive field.
Ms (Am2/kg) Mr /Ms Hc (kA/m)
77 K 300 K 77 K 300 K 77 K 300 KTc (°C)
Sample 1 80 76 0.32 0.34 33.9 31.8 598Sample 2 72 65 0.30 0.30 28.2 22.1 608Sample 3 58 54 0.26 0.28 28.8 24.4 607Sample 4 40 39 0.27 0.28 33.8 31.1 607Sample 5 32 29 0.28 0.31 34.3 32.2 607
FeNi@SiO2FeNi
TEOSNH4OH
Ultrasound90 min
Ethanol
Ultrasound90 min
FeNi
Si OSiO
Si
OH
OH
O
OH
O
Figure 1
22
Page 23
Figure 2
Figure 3
23
Page 25
Figure 5
Figure 6
25
Page 26
Figure 7
Figure 8
26